Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


## NULL

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta3_pH 1 1.423884
beta2_pelagic 4 1.382053
beta3_yellow 2 1.368928
beta3_black 2 1.335127
beta2_yellow 10 1.300154
beta1_black 9 1.294237
tau_beta0_pH 1 1.274468
beta0_black 6 1.273418
beta1_yellow 3 1.221398
beta2_black 6 1.219130
parameter n badRhat_avg
tau_beta0_pelagic 1 1.209031
beta0_yellow 2 1.203331
beta1_pH 11 1.197594
beta1_pelagic 4 1.192629
beta3_pelagic 2 1.186307
beta2_pH 3 1.183494
beta0_pH 2 1.172832
beta0_pelagic 2 1.144044
tau_beta0_yellow 1 1.135039
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta0_black 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0
beta0_pelagic 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0
beta0_pH 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1
beta0_yellow 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
beta1_black 1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 0
beta1_pelagic 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1
beta1_pH 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 1
beta1_yellow 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1
beta2_black 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 0
beta2_pelagic 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0
beta2_pH 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0
beta2_yellow 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0
beta3_black 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0
beta3_pelagic 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0
beta3_pH 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
beta3_yellow 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0
tau_beta0_pelagic 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
tau_beta0_yellow 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.136 0.072 -0.267 -0.139 0.010
mu_bc_H[2] -0.097 0.045 -0.173 -0.101 -0.001
mu_bc_H[3] -0.434 0.072 -0.573 -0.438 -0.286
mu_bc_H[4] -0.986 0.196 -1.390 -0.981 -0.608
mu_bc_H[5] 0.913 1.030 -0.175 0.689 3.330
mu_bc_H[6] -2.223 0.326 -2.842 -2.227 -1.581
mu_bc_H[7] -0.473 0.114 -0.704 -0.470 -0.261
mu_bc_H[8] 0.256 0.360 -0.324 0.213 1.082
mu_bc_H[9] -0.305 0.135 -0.563 -0.303 -0.037
mu_bc_H[10] -0.117 0.068 -0.241 -0.120 0.022
mu_bc_H[11] -0.105 0.041 -0.182 -0.106 -0.020
mu_bc_H[12] -0.246 0.102 -0.462 -0.241 -0.049
mu_bc_H[13] -0.126 0.078 -0.278 -0.126 0.032
mu_bc_H[14] -0.286 0.094 -0.478 -0.285 -0.102
mu_bc_H[15] -0.349 0.054 -0.453 -0.349 -0.241
mu_bc_H[16] -0.232 0.382 -0.890 -0.256 0.608
mu_bc_R[1] 1.348 0.141 1.064 1.343 1.629
mu_bc_R[2] 1.491 0.087 1.317 1.492 1.660
mu_bc_R[3] 1.431 0.136 1.158 1.433 1.690
mu_bc_R[4] 0.989 0.194 0.581 1.002 1.337
mu_bc_R[5] 1.147 0.454 0.250 1.145 2.021
mu_bc_R[6] -1.558 0.433 -2.390 -1.562 -0.732
mu_bc_R[7] 0.291 0.187 -0.076 0.293 0.655
mu_bc_R[8] 0.533 0.196 0.138 0.536 0.899
mu_bc_R[9] 0.383 0.200 -0.051 0.398 0.728
mu_bc_R[10] 1.322 0.128 1.064 1.327 1.568
mu_bc_R[11] 1.144 0.080 0.991 1.144 1.304
mu_bc_R[12] 0.933 0.202 0.523 0.933 1.320
mu_bc_R[13] 1.089 0.100 0.894 1.091 1.282
mu_bc_R[14] 0.986 0.141 0.711 0.986 1.261
mu_bc_R[15] 0.917 0.098 0.730 0.915 1.103
mu_bc_R[16] 1.183 0.120 0.948 1.183 1.416
tau_pH[1] 2.742 0.259 2.260 2.728 3.294
tau_pH[2] 2.641 0.315 2.088 2.628 3.301
tau_pH[3] 3.099 0.339 2.487 3.079 3.819
beta0_pH[1,1] 0.556 0.228 0.085 0.562 0.984
beta0_pH[2,1] 1.311 0.224 0.857 1.315 1.736
beta0_pH[3,1] 1.385 0.249 0.848 1.396 1.856
beta0_pH[4,1] 1.658 0.271 1.070 1.673 2.135
beta0_pH[5,1] -0.468 0.452 -1.242 -0.495 0.658
beta0_pH[6,1] 0.191 0.534 -0.936 0.221 1.074
beta0_pH[7,1] 0.451 0.489 -0.622 0.649 1.038
beta0_pH[8,1] -0.578 0.338 -1.392 -0.509 -0.079
beta0_pH[9,1] -0.470 0.294 -1.096 -0.459 0.076
beta0_pH[10,1] 0.329 0.237 -0.120 0.332 0.789
beta0_pH[11,1] -0.251 0.250 -0.772 -0.232 0.201
beta0_pH[12,1] 0.387 0.280 -0.195 0.397 0.902
beta0_pH[13,1] -0.136 0.220 -0.618 -0.125 0.268
beta0_pH[14,1] -0.367 0.251 -0.881 -0.357 0.105
beta0_pH[15,1] -0.486 0.288 -1.118 -0.461 0.012
beta0_pH[16,1] -0.539 0.332 -1.320 -0.511 0.024
beta0_pH[1,2] 2.656 0.226 2.145 2.683 3.025
beta0_pH[2,2] 2.886 0.201 2.406 2.905 3.234
beta0_pH[3,2] 2.418 0.295 1.777 2.447 2.918
beta0_pH[4,2] 2.606 0.284 1.894 2.675 2.992
beta0_pH[5,2] 4.536 1.512 2.349 4.271 8.337
beta0_pH[6,2] 2.848 0.291 2.311 2.865 3.367
beta0_pH[7,2] 1.897 0.199 1.477 1.914 2.219
beta0_pH[8,2] 2.797 0.220 2.379 2.815 3.127
beta0_pH[9,2] 2.884 0.599 1.642 3.052 3.707
beta0_pH[10,2] 3.651 0.262 3.039 3.677 4.052
beta0_pH[11,2] -4.827 0.276 -5.363 -4.823 -4.280
beta0_pH[12,2] -4.803 0.424 -5.692 -4.780 -4.048
beta0_pH[13,2] -4.607 0.367 -5.360 -4.608 -3.908
beta0_pH[14,2] -5.556 0.453 -6.470 -5.545 -4.707
beta0_pH[15,2] -4.157 0.312 -4.770 -4.147 -3.544
beta0_pH[16,2] -4.807 0.360 -5.529 -4.803 -4.114
beta0_pH[1,3] 1.250 0.315 0.431 1.294 1.710
beta0_pH[2,3] 1.936 0.388 0.998 2.045 2.436
beta0_pH[3,3] 2.098 0.414 1.196 2.141 2.704
beta0_pH[4,3] 2.468 0.571 1.134 2.681 3.140
beta0_pH[5,3] 1.255 2.445 -4.077 1.221 6.609
beta0_pH[6,3] -1.105 1.467 -2.513 -1.561 2.982
beta0_pH[7,3] -2.074 0.759 -3.585 -2.043 -0.680
beta0_pH[8,3] 0.297 0.169 -0.039 0.296 0.629
beta0_pH[9,3] -0.062 0.313 -0.664 -0.070 0.560
beta0_pH[10,3] 0.807 0.289 0.216 0.827 1.293
beta0_pH[11,3] -0.115 0.310 -0.749 -0.110 0.476
beta0_pH[12,3] -1.004 0.329 -1.690 -0.994 -0.395
beta0_pH[13,3] -0.024 0.287 -0.591 -0.024 0.513
beta0_pH[14,3] -0.128 0.238 -0.593 -0.131 0.334
beta0_pH[15,3] -0.693 0.316 -1.320 -0.664 -0.132
beta0_pH[16,3] -0.370 0.256 -0.878 -0.371 0.139
beta1_pH[1,1] 3.070 0.420 2.335 3.047 3.955
beta1_pH[2,1] 2.471 0.411 1.793 2.431 3.437
beta1_pH[3,1] 2.583 0.482 1.811 2.532 3.680
beta1_pH[4,1] 3.000 0.563 2.166 2.920 4.402
beta1_pH[5,1] 2.017 0.462 1.127 2.003 2.991
beta1_pH[6,1] 2.536 0.845 1.272 2.379 4.644
beta1_pH[7,1] 2.139 1.330 0.396 2.009 4.806
beta1_pH[8,1] 3.453 1.140 2.145 3.120 6.563
beta1_pH[9,1] 2.107 0.379 1.426 2.090 2.927
beta1_pH[10,1] 2.236 0.334 1.599 2.219 2.902
beta1_pH[11,1] 6.614 0.815 5.280 6.538 8.460
beta1_pH[12,1] 3.000 0.333 2.382 2.985 3.689
beta1_pH[13,1] 5.660 1.031 4.141 5.487 8.088
beta1_pH[14,1] 14.472 4.001 9.014 13.498 24.019
beta1_pH[15,1] 8.298 1.911 5.602 7.858 12.786
beta1_pH[16,1] 12.536 1.582 9.429 12.554 15.514
beta1_pH[1,2] 5.087 23.757 0.005 1.020 29.797
beta1_pH[2,2] 5.148 16.370 0.007 1.133 35.301
beta1_pH[3,2] 1.244 0.348 0.614 1.221 1.959
beta1_pH[4,2] 3.824 9.528 0.009 1.028 27.870
beta1_pH[5,2] 3.656 17.223 0.000 0.287 26.865
beta1_pH[6,2] 1.106 2.116 0.000 0.900 3.331
beta1_pH[7,2] 0.819 2.105 0.000 0.132 6.543
beta1_pH[8,2] 0.680 1.925 0.000 0.093 4.415
beta1_pH[9,2] 0.834 1.182 0.000 0.648 2.440
beta1_pH[10,2] 3.764 8.926 0.000 0.938 28.275
beta1_pH[11,2] 6.688 0.302 6.106 6.682 7.274
beta1_pH[12,2] 6.641 0.539 5.718 6.584 7.847
beta1_pH[13,2] 7.073 0.403 6.292 7.064 7.883
beta1_pH[14,2] 7.440 0.483 6.522 7.432 8.436
beta1_pH[15,2] 6.687 0.331 6.033 6.683 7.340
beta1_pH[16,2] 7.524 0.388 6.773 7.529 8.301
beta1_pH[1,3] 2.072 0.550 1.297 1.995 3.479
beta1_pH[2,3] 1.223 2.477 0.001 0.576 10.833
beta1_pH[3,3] 1.130 2.284 0.001 0.652 10.380
beta1_pH[4,3] 1.025 2.125 0.001 0.561 5.106
beta1_pH[5,3] 5.342 11.153 1.489 3.003 26.047
beta1_pH[6,3] 3.856 4.002 1.610 2.963 12.117
beta1_pH[7,3] 2.925 0.724 1.623 2.878 4.461
beta1_pH[8,3] 2.723 0.298 2.145 2.722 3.299
beta1_pH[9,3] 2.158 0.368 1.424 2.169 2.861
beta1_pH[10,3] 2.573 0.357 1.951 2.551 3.303
beta1_pH[11,3] 2.801 0.359 2.122 2.786 3.536
beta1_pH[12,3] 4.354 0.400 3.594 4.344 5.175
beta1_pH[13,3] 2.175 0.320 1.547 2.176 2.796
beta1_pH[14,3] 2.621 0.291 2.057 2.624 3.179
beta1_pH[15,3] 2.538 0.341 1.909 2.514 3.255
beta1_pH[16,3] 2.165 0.295 1.551 2.172 2.742
beta2_pH[1,1] 0.506 0.227 0.261 0.466 0.974
beta2_pH[2,1] 0.529 0.450 0.182 0.446 1.322
beta2_pH[3,1] 0.463 0.345 0.173 0.393 1.174
beta2_pH[4,1] 0.402 0.197 0.172 0.366 0.813
beta2_pH[5,1] 1.184 1.512 0.068 0.648 5.110
beta2_pH[6,1] 0.760 1.318 0.111 0.336 4.768
beta2_pH[7,1] -0.644 1.531 -4.686 -0.056 1.043
beta2_pH[8,1] 0.365 0.436 0.121 0.300 0.931
beta2_pH[9,1] 0.677 0.859 0.182 0.480 2.750
beta2_pH[10,1] 0.828 0.805 0.270 0.629 2.617
beta2_pH[11,1] 0.234 0.046 0.157 0.230 0.337
beta2_pH[12,1] 0.931 0.478 0.386 0.806 2.171
beta2_pH[13,1] 0.267 0.068 0.162 0.259 0.426
beta2_pH[14,1] 0.253 0.039 0.190 0.249 0.338
beta2_pH[15,1] 0.206 0.049 0.133 0.199 0.318
beta2_pH[16,1] 0.162 0.022 0.124 0.160 0.211
beta2_pH[1,2] -2.057 4.189 -10.410 -2.089 6.501
beta2_pH[2,2] -3.603 3.183 -10.910 -3.118 1.474
beta2_pH[3,2] -3.948 2.700 -10.944 -3.310 -0.611
beta2_pH[4,2] -3.864 2.997 -10.766 -3.428 0.983
beta2_pH[5,2] -1.903 4.088 -9.608 -2.061 7.041
beta2_pH[6,2] -2.674 3.735 -10.073 -2.690 6.437
beta2_pH[7,2] -2.540 3.889 -10.218 -2.655 6.400
beta2_pH[8,2] -2.424 3.937 -10.019 -2.538 6.566
beta2_pH[9,2] -2.808 3.790 -10.214 -2.883 6.010
beta2_pH[10,2] -3.077 3.810 -10.555 -3.148 5.664
beta2_pH[11,2] -7.348 2.568 -13.397 -6.845 -3.803
beta2_pH[12,2] -3.732 2.823 -10.396 -3.030 -0.608
beta2_pH[13,2] -4.144 2.458 -10.560 -3.375 -1.394
beta2_pH[14,2] -5.034 2.422 -10.916 -4.549 -1.838
beta2_pH[15,2] -6.980 2.467 -12.940 -6.516 -3.563
beta2_pH[16,2] -7.282 2.630 -13.965 -6.785 -3.618
beta2_pH[1,3] 2.796 2.244 0.273 2.281 8.585
beta2_pH[2,3] 1.245 3.823 -6.942 1.235 8.979
beta2_pH[3,3] 0.180 4.250 -8.118 0.013 8.969
beta2_pH[4,3] 1.249 3.864 -7.046 1.243 8.865
beta2_pH[5,3] 5.446 2.973 0.251 5.341 11.872
beta2_pH[6,3] 5.656 2.919 0.784 5.450 12.030
beta2_pH[7,3] 5.409 2.961 0.781 5.155 12.320
beta2_pH[8,3] 6.828 2.771 2.511 6.455 13.656
beta2_pH[9,3] 5.727 2.560 1.615 5.492 11.290
beta2_pH[10,3] 5.458 2.862 0.693 5.252 11.550
beta2_pH[11,3] -1.402 0.677 -2.955 -1.289 -0.597
beta2_pH[12,3] -1.595 0.656 -2.938 -1.472 -0.899
beta2_pH[13,3] -1.774 0.983 -4.176 -1.571 -0.737
beta2_pH[14,3] -1.752 0.870 -3.786 -1.557 -0.835
beta2_pH[15,3] -1.783 0.870 -4.089 -1.590 -0.804
beta2_pH[16,3] -1.755 0.940 -4.456 -1.534 -0.795
beta3_pH[1,1] 35.740 1.066 33.779 35.717 37.925
beta3_pH[2,1] 34.408 1.757 31.478 34.226 38.585
beta3_pH[3,1] 35.813 1.967 32.521 35.595 40.305
beta3_pH[4,1] 36.102 1.826 32.909 35.972 39.941
beta3_pH[5,1] 29.251 3.244 23.239 28.286 36.469
beta3_pH[6,1] 40.431 3.587 32.397 41.423 45.295
beta3_pH[7,1] 28.191 9.438 18.327 23.735 45.678
beta3_pH[8,1] 39.111 2.385 35.005 38.892 44.845
beta3_pH[9,1] 31.192 2.105 27.785 30.956 36.045
beta3_pH[10,1] 32.796 1.171 30.639 32.723 35.308
beta3_pH[11,1] 35.529 1.327 33.152 35.468 38.397
beta3_pH[12,1] 30.310 0.653 28.945 30.336 31.452
beta3_pH[13,1] 38.243 1.850 35.121 38.024 42.443
beta3_pH[14,1] 41.297 1.865 38.223 41.051 45.303
beta3_pH[15,1] 39.604 2.520 35.630 39.244 45.007
beta3_pH[16,1] 43.975 1.408 40.945 44.215 45.897
beta3_pH[1,2] 30.397 8.716 18.604 28.112 44.680
beta3_pH[2,2] 28.880 6.207 18.827 28.472 43.235
beta3_pH[3,2] 41.749 1.521 39.637 41.837 44.089
beta3_pH[4,2] 29.599 9.077 18.446 25.644 44.820
beta3_pH[5,2] 30.370 8.214 18.432 29.473 45.190
beta3_pH[6,2] 33.039 6.135 18.961 34.978 44.201
beta3_pH[7,2] 29.329 7.600 18.471 28.481 44.815
beta3_pH[8,2] 28.871 7.407 18.373 27.798 44.132
beta3_pH[9,2] 36.700 9.306 18.907 42.563 45.700
beta3_pH[10,2] 30.809 6.720 19.073 29.811 43.895
beta3_pH[11,2] 43.386 0.150 43.133 43.373 43.708
beta3_pH[12,2] 43.163 0.226 42.611 43.166 43.589
beta3_pH[13,2] 43.834 0.140 43.511 43.853 44.050
beta3_pH[14,2] 43.315 0.161 43.074 43.291 43.688
beta3_pH[15,2] 43.400 0.158 43.144 43.387 43.742
beta3_pH[16,2] 43.482 0.159 43.195 43.478 43.783
beta3_pH[1,3] 39.953 1.022 37.244 40.048 41.515
beta3_pH[2,3] 30.592 7.218 18.686 31.404 44.533
beta3_pH[3,3] 32.801 7.996 18.644 32.615 44.484
beta3_pH[4,3] 27.506 7.023 18.327 26.270 44.223
beta3_pH[5,3] 27.046 6.292 18.349 26.630 41.822
beta3_pH[6,3] 30.679 4.220 20.305 31.701 39.539
beta3_pH[7,3] 25.426 1.821 22.824 24.925 29.344
beta3_pH[8,3] 41.503 0.207 41.123 41.507 41.890
beta3_pH[9,3] 33.746 0.439 33.013 33.772 34.589
beta3_pH[10,3] 36.106 0.465 34.926 36.129 36.838
beta3_pH[11,3] 41.624 0.701 40.244 41.623 42.985
beta3_pH[12,3] 41.754 0.336 41.083 41.758 42.406
beta3_pH[13,3] 42.140 0.685 40.878 42.125 43.529
beta3_pH[14,3] 40.848 0.519 39.814 40.859 41.814
beta3_pH[15,3] 42.154 0.667 40.825 42.220 43.401
beta3_pH[16,3] 42.393 0.691 40.934 42.435 43.627
beta0_pelagic[1] 1.854 0.652 -0.272 2.089 2.417
beta0_pelagic[2] 1.403 0.285 0.602 1.474 1.744
beta0_pelagic[3] 0.203 0.406 -0.805 0.272 0.816
beta0_pelagic[4] 0.156 0.579 -1.228 0.242 1.085
beta0_pelagic[5] 0.172 1.549 -3.004 1.166 1.673
beta0_pelagic[6] 1.563 0.197 1.126 1.585 1.852
beta0_pelagic[7] 1.528 0.140 1.265 1.534 1.784
beta0_pelagic[8] 1.850 0.140 1.552 1.860 2.101
beta0_pelagic[9] 2.039 0.795 0.126 2.292 2.866
beta0_pelagic[10] 2.572 0.146 2.291 2.579 2.831
beta0_pelagic[11] 0.649 0.131 0.393 0.646 0.903
beta0_pelagic[12] 1.754 0.133 1.491 1.753 2.012
beta0_pelagic[13] 0.511 0.158 0.186 0.517 0.785
beta0_pelagic[14] 0.390 0.178 0.006 0.402 0.704
beta0_pelagic[15] -0.276 0.138 -0.548 -0.279 -0.003
beta0_pelagic[16] 0.580 0.132 0.304 0.584 0.818
beta1_pelagic[1] 0.389 0.656 0.000 0.070 2.508
beta1_pelagic[2] 0.193 0.309 0.000 0.041 1.130
beta1_pelagic[3] 0.879 0.528 0.013 0.779 2.209
beta1_pelagic[4] 1.028 0.600 0.000 0.969 2.421
beta1_pelagic[5] 1.308 1.669 0.000 0.027 4.696
beta1_pelagic[6] 0.107 0.344 0.000 0.001 0.911
beta1_pelagic[7] 6.512 22.558 0.000 0.003 96.396
beta1_pelagic[8] 0.179 0.721 0.000 0.002 1.260
beta1_pelagic[9] 0.803 0.941 0.000 0.632 3.117
beta1_pelagic[10] 0.093 0.366 0.000 0.001 0.833
beta1_pelagic[11] 2.477 0.300 1.963 2.458 3.147
beta1_pelagic[12] 2.642 0.266 2.126 2.643 3.176
beta1_pelagic[13] 2.386 0.482 1.591 2.333 3.542
beta1_pelagic[14] 3.184 0.688 2.236 3.041 4.991
beta1_pelagic[15] 2.586 0.234 2.116 2.590 3.031
beta1_pelagic[16] 2.999 0.298 2.504 2.984 3.503
beta2_pelagic[1] 1.757 2.861 -4.134 1.283 8.258
beta2_pelagic[2] 1.719 2.856 -3.946 1.263 8.261
beta2_pelagic[3] 1.692 2.262 0.065 0.719 8.678
beta2_pelagic[4] 2.138 2.452 0.099 1.344 8.309
beta2_pelagic[5] -1.804 3.714 -8.587 -2.227 6.869
beta2_pelagic[6] -0.756 4.015 -8.892 -0.905 7.436
beta2_pelagic[7] -1.519 4.020 -9.419 -1.815 7.244
beta2_pelagic[8] -1.324 3.885 -8.904 -1.491 7.285
beta2_pelagic[9] 0.553 3.531 -6.865 0.585 7.978
beta2_pelagic[10] -1.855 3.022 -5.732 -1.927 6.086
beta2_pelagic[11] 3.193 2.671 0.732 2.045 10.590
beta2_pelagic[12] 4.956 2.496 1.935 4.298 11.897
beta2_pelagic[13] 1.262 1.472 0.271 0.747 5.639
beta2_pelagic[14] 0.532 0.343 0.220 0.463 1.153
beta2_pelagic[15] 5.610 2.927 1.972 4.918 13.621
beta2_pelagic[16] 5.164 2.777 0.887 4.741 11.943
beta3_pelagic[1] 27.673 7.926 18.410 24.705 44.946
beta3_pelagic[2] 28.526 8.254 18.373 25.948 44.943
beta3_pelagic[3] 29.095 4.714 21.044 28.862 41.416
beta3_pelagic[4] 25.334 4.102 20.088 24.724 39.494
beta3_pelagic[5] 36.331 9.884 18.907 39.368 45.992
beta3_pelagic[6] 29.947 7.882 18.440 29.049 44.838
beta3_pelagic[7] 27.873 8.349 18.350 25.641 44.744
beta3_pelagic[8] 29.760 7.610 18.623 28.703 44.748
beta3_pelagic[9] 29.244 6.440 18.832 27.652 43.871
beta3_pelagic[10] 29.543 8.057 18.406 28.585 44.852
beta3_pelagic[11] 43.173 0.404 42.251 43.193 43.891
beta3_pelagic[12] 43.473 0.230 43.054 43.466 43.916
beta3_pelagic[13] 42.685 1.053 40.647 42.754 44.754
beta3_pelagic[14] 42.996 1.258 40.501 43.012 45.515
beta3_pelagic[15] 43.228 0.242 42.664 43.229 43.671
beta3_pelagic[16] 43.256 0.274 42.589 43.263 43.710
mu_beta0_pelagic[1] 0.808 0.876 -1.153 0.872 2.512
mu_beta0_pelagic[2] 1.574 0.682 -0.160 1.714 2.565
mu_beta0_pelagic[3] 0.600 0.413 -0.231 0.598 1.429
tau_beta0_pelagic[1] 1.172 2.971 0.063 0.583 5.017
tau_beta0_pelagic[2] 2.075 2.656 0.077 1.152 9.423
tau_beta0_pelagic[3] 1.872 1.394 0.222 1.546 5.478
beta0_yellow[1] -0.539 0.197 -0.965 -0.522 -0.224
beta0_yellow[2] 0.503 0.150 0.175 0.508 0.778
beta0_yellow[3] -0.314 0.171 -0.675 -0.308 0.004
beta0_yellow[4] 0.865 0.225 0.301 0.898 1.192
beta0_yellow[5] -1.233 0.415 -2.056 -1.224 -0.436
beta0_yellow[6] 0.241 0.207 -0.168 0.239 0.652
beta0_yellow[7] 0.775 0.704 -1.364 1.012 1.326
beta0_yellow[8] 0.617 0.820 -1.610 0.942 1.277
beta0_yellow[9] -0.049 0.299 -0.594 -0.055 0.565
beta0_yellow[10] 0.243 0.146 -0.049 0.244 0.523
beta0_yellow[11] -1.635 0.657 -2.673 -1.764 -0.074
beta0_yellow[12] -3.597 0.433 -4.550 -3.572 -2.832
beta0_yellow[13] -3.523 0.448 -4.494 -3.492 -2.731
beta0_yellow[14] -1.931 0.568 -2.828 -1.997 -0.306
beta0_yellow[15] -2.836 0.426 -3.715 -2.815 -2.010
beta0_yellow[16] -2.300 0.398 -3.068 -2.299 -1.529
beta1_yellow[1] 0.495 0.654 0.000 0.354 1.712
beta1_yellow[2] 1.049 0.305 0.605 1.022 1.697
beta1_yellow[3] 0.667 0.240 0.185 0.660 1.180
beta1_yellow[4] 1.309 0.636 0.644 1.164 3.324
beta1_yellow[5] 3.069 1.921 1.366 2.811 5.931
beta1_yellow[6] 2.298 0.352 1.619 2.290 2.995
beta1_yellow[7] 7.899 13.539 0.358 3.830 37.215
beta1_yellow[8] 3.657 5.575 0.019 2.006 25.075
beta1_yellow[9] 1.548 0.484 0.775 1.519 2.575
beta1_yellow[10] 2.623 0.491 1.765 2.592 3.660
beta1_yellow[11] 1.982 0.529 0.952 1.978 2.914
beta1_yellow[12] 2.376 0.436 1.623 2.345 3.369
beta1_yellow[13] 2.706 0.446 1.946 2.669 3.688
beta1_yellow[14] 2.053 0.486 1.015 2.078 2.974
beta1_yellow[15] 2.144 0.421 1.323 2.139 3.019
beta1_yellow[16] 2.107 0.399 1.327 2.095 2.891
beta2_yellow[1] -4.155 3.102 -9.826 -3.853 0.611
beta2_yellow[2] -3.682 2.735 -9.917 -3.182 -0.249
beta2_yellow[3] -3.590 2.726 -9.783 -3.026 -0.188
beta2_yellow[4] -3.250 2.786 -9.771 -2.693 -0.119
beta2_yellow[5] -4.345 2.839 -11.058 -3.835 -0.507
beta2_yellow[6] 3.673 2.251 0.915 3.133 9.301
beta2_yellow[7] -3.547 4.265 -11.489 -3.836 6.670
beta2_yellow[8] -1.871 4.310 -10.180 -1.889 7.615
beta2_yellow[9] 3.767 2.718 0.121 3.498 9.716
beta2_yellow[10] -4.891 2.828 -11.620 -4.367 -1.002
beta2_yellow[11] -3.766 2.576 -10.752 -3.169 -0.253
beta2_yellow[12] -4.321 2.480 -10.734 -3.642 -1.364
beta2_yellow[13] -4.975 3.425 -13.734 -3.643 -1.521
beta2_yellow[14] -4.197 2.766 -11.396 -3.501 -0.172
beta2_yellow[15] -3.795 2.359 -10.350 -3.154 -1.030
beta2_yellow[16] -4.368 2.508 -10.926 -3.591 -1.430
beta3_yellow[1] 28.368 7.540 18.386 26.949 44.717
beta3_yellow[2] 29.133 1.564 26.870 28.889 32.654
beta3_yellow[3] 33.086 2.507 28.893 32.966 38.429
beta3_yellow[4] 28.842 3.045 22.915 27.960 35.307
beta3_yellow[5] 33.365 1.491 30.336 33.423 35.796
beta3_yellow[6] 39.653 0.531 38.722 39.624 40.874
beta3_yellow[7] 21.366 3.742 18.577 20.193 31.903
beta3_yellow[8] 25.692 5.478 18.278 25.235 41.018
beta3_yellow[9] 37.571 2.638 33.333 37.614 42.787
beta3_yellow[10] 29.355 0.431 28.322 29.393 30.004
beta3_yellow[11] 43.509 4.796 29.643 45.350 45.968
beta3_yellow[12] 43.365 0.425 42.577 43.325 44.298
beta3_yellow[13] 44.839 0.407 43.980 44.920 45.560
beta3_yellow[14] 43.583 2.994 31.054 44.171 45.853
beta3_yellow[15] 45.328 0.494 44.252 45.396 45.975
beta3_yellow[16] 44.604 0.628 43.454 44.610 45.807
mu_beta0_yellow[1] 0.130 0.572 -1.078 0.122 1.310
mu_beta0_yellow[2] 0.108 0.510 -0.992 0.120 1.097
mu_beta0_yellow[3] -2.298 0.674 -3.304 -2.417 -0.593
tau_beta0_yellow[1] 1.722 1.917 0.094 1.113 6.704
tau_beta0_yellow[2] 1.415 2.430 0.144 0.975 4.893
tau_beta0_yellow[3] 1.368 1.702 0.096 0.880 5.441
beta0_black[1] -0.079 0.150 -0.360 -0.082 0.216
beta0_black[2] 1.833 0.316 1.420 1.868 2.130
beta0_black[3] 1.251 0.186 0.853 1.271 1.540
beta0_black[4] 1.988 0.325 1.204 2.020 2.453
beta0_black[5] 1.570 1.922 -2.710 1.662 5.357
beta0_black[6] 1.574 1.959 -2.789 1.637 5.455
beta0_black[7] 1.633 1.967 -2.708 1.676 5.746
beta0_black[8] 1.270 0.214 0.860 1.266 1.675
beta0_black[9] 2.412 0.264 1.882 2.426 2.909
beta0_black[10] 1.463 0.130 1.208 1.461 1.712
beta0_black[11] 3.394 0.270 2.880 3.423 3.738
beta0_black[12] 4.473 0.189 4.116 4.469 4.838
beta0_black[13] -0.097 0.210 -0.518 -0.095 0.316
beta0_black[14] 2.342 0.544 0.899 2.404 3.057
beta0_black[15] 1.157 0.317 0.353 1.219 1.556
beta0_black[16] 3.873 0.976 0.984 4.186 4.536
beta2_black[1] 3.592 2.378 0.729 3.022 9.416
beta2_black[2] 0.166 4.443 -8.111 -0.291 9.292
beta2_black[3] 0.603 4.139 -8.043 0.715 8.526
beta2_black[4] -2.627 2.610 -8.766 -2.138 0.736
beta2_black[5] -0.280 4.355 -9.105 -0.266 8.236
beta2_black[6] -0.219 4.408 -9.141 -0.278 8.523
beta2_black[7] -0.108 4.288 -8.526 -0.149 8.449
beta2_black[8] -0.170 4.386 -8.883 -0.118 8.624
beta2_black[9] -0.248 4.310 -8.971 -0.140 8.386
beta2_black[10] -0.209 4.419 -9.163 -0.191 8.415
beta2_black[11] -2.159 2.714 -8.736 -1.547 2.200
beta2_black[12] -3.627 2.268 -8.006 -3.013 -0.661
beta2_black[13] -2.815 2.258 -8.916 -2.030 -0.505
beta2_black[14] -2.147 2.759 -8.700 -1.284 1.831
beta2_black[15] -2.428 2.887 -8.829 -1.977 3.017
beta2_black[16] -1.734 3.296 -8.749 -1.485 4.739
beta3_black[1] 41.693 1.418 40.085 41.862 43.071
beta3_black[2] 30.041 7.995 18.409 30.062 44.599
beta3_black[3] 29.783 7.878 18.423 29.476 44.901
beta3_black[4] 32.923 3.649 21.623 32.799 39.473
beta3_black[5] 30.121 7.937 18.555 29.473 44.882
beta3_black[6] 30.155 7.896 18.359 29.355 44.893
beta3_black[7] 30.035 7.932 18.483 29.109 44.735
beta3_black[8] 30.044 8.022 18.526 29.067 44.936
beta3_black[9] 29.853 7.974 18.463 28.804 44.940
beta3_black[10] 29.740 7.843 18.511 28.638 44.950
beta3_black[11] 30.266 7.131 18.589 30.072 44.202
beta3_black[12] 32.895 0.875 31.078 32.996 33.887
beta3_black[13] 39.332 0.650 37.872 39.399 40.428
beta3_black[14] 35.644 6.502 19.331 37.640 44.916
beta3_black[15] 32.108 7.896 18.847 32.026 45.236
beta3_black[16] 29.045 7.686 18.405 27.680 44.873
beta4_black[1] -0.250 0.186 -0.610 -0.247 0.112
beta4_black[2] 0.246 0.174 -0.095 0.250 0.593
beta4_black[3] -0.934 0.188 -1.307 -0.935 -0.567
beta4_black[4] 0.554 0.220 0.123 0.552 0.991
beta4_black[5] 0.241 2.413 -4.357 0.120 4.992
beta4_black[6] 0.300 2.536 -3.981 0.161 5.264
beta4_black[7] 0.163 2.896 -4.396 0.118 5.196
beta4_black[8] -0.692 0.351 -1.381 -0.684 -0.003
beta4_black[9] 1.479 1.024 -0.102 1.335 3.918
beta4_black[10] 0.025 0.183 -0.344 0.029 0.375
beta4_black[11] -0.690 0.208 -1.101 -0.690 -0.284
beta4_black[12] 0.313 0.325 -0.299 0.308 0.958
beta4_black[13] -1.201 0.209 -1.612 -1.198 -0.803
beta4_black[14] -0.138 0.223 -0.565 -0.139 0.303
beta4_black[15] -0.887 0.201 -1.292 -0.882 -0.506
beta4_black[16] -0.588 0.218 -1.032 -0.582 -0.165
mu_beta0_black[1] 1.183 0.835 -0.676 1.222 2.816
mu_beta0_black[2] 1.593 0.888 -0.458 1.639 3.299
mu_beta0_black[3] 2.271 0.996 0.110 2.332 4.131
tau_beta0_black[1] 0.796 0.778 0.061 0.552 2.859
tau_beta0_black[2] 1.994 4.151 0.058 0.850 10.031
tau_beta0_black[3] 0.257 0.175 0.053 0.211 0.699
beta0_dsr[11] -3.041 0.265 -3.580 -3.046 -2.521
beta0_dsr[12] 4.479 0.274 3.940 4.479 5.010
beta0_dsr[13] -1.589 0.278 -2.139 -1.586 -1.050
beta0_dsr[14] -4.120 0.453 -5.032 -4.109 -3.277
beta0_dsr[15] -2.410 0.261 -2.926 -2.410 -1.911
beta0_dsr[16] -3.050 0.356 -3.758 -3.042 -2.359
beta1_dsr[11] 4.922 0.276 4.379 4.916 5.461
beta1_dsr[12] 6.239 4.668 2.425 5.109 17.460
beta1_dsr[13] 3.048 0.282 2.513 3.038 3.623
beta1_dsr[14] 6.751 0.487 5.839 6.747 7.718
beta1_dsr[15] 3.606 0.263 3.093 3.603 4.133
beta1_dsr[16] 5.835 0.372 5.108 5.836 6.563
beta2_dsr[11] -8.355 2.455 -13.997 -7.975 -4.649
beta2_dsr[12] -7.190 2.657 -13.245 -6.949 -2.585
beta2_dsr[13] -6.511 2.707 -12.556 -6.318 -1.922
beta2_dsr[14] -6.970 2.800 -13.803 -6.510 -2.670
beta2_dsr[15] -7.829 2.494 -13.657 -7.495 -3.908
beta2_dsr[16] -8.008 2.364 -13.428 -7.665 -4.404
beta3_dsr[11] 43.484 0.144 43.218 43.479 43.759
beta3_dsr[12] 34.018 0.629 32.320 34.152 34.800
beta3_dsr[13] 43.234 0.240 42.901 43.176 43.818
beta3_dsr[14] 43.255 0.140 43.077 43.225 43.622
beta3_dsr[15] 43.472 0.187 43.143 43.463 43.832
beta3_dsr[16] 43.439 0.157 43.170 43.430 43.757
beta4_dsr[11] 0.666 0.209 0.257 0.664 1.079
beta4_dsr[12] 0.303 0.468 -0.586 0.305 1.292
beta4_dsr[13] -0.083 0.208 -0.504 -0.081 0.308
beta4_dsr[14] 0.202 0.248 -0.289 0.207 0.675
beta4_dsr[15] 0.983 0.209 0.567 0.984 1.399
beta4_dsr[16] 0.178 0.216 -0.243 0.177 0.601
beta0_slope[11] -2.006 0.155 -2.312 -2.008 -1.701
beta0_slope[12] -4.678 0.267 -5.205 -4.668 -4.173
beta0_slope[13] -1.443 0.227 -2.012 -1.417 -1.100
beta0_slope[14] -2.637 0.203 -3.028 -2.640 -2.237
beta0_slope[15] -1.700 0.159 -2.003 -1.707 -1.384
beta0_slope[16] -2.767 0.166 -3.092 -2.767 -2.448
beta1_slope[11] 4.376 0.290 3.795 4.371 4.940
beta1_slope[12] 4.782 0.535 3.728 4.775 5.833
beta1_slope[13] 2.739 0.606 2.001 2.620 4.581
beta1_slope[14] 6.023 0.824 4.644 5.938 7.929
beta1_slope[15] 2.020 0.272 1.486 2.027 2.545
beta1_slope[16] 5.297 0.387 4.548 5.287 6.069
beta2_slope[11] 7.759 2.339 4.063 7.487 13.155
beta2_slope[12] 6.490 2.677 2.034 6.190 12.489
beta2_slope[13] 4.545 3.019 0.287 4.205 11.216
beta2_slope[14] 2.838 2.607 0.736 1.523 9.642
beta2_slope[15] 6.638 2.589 2.553 6.342 12.281
beta2_slope[16] 7.322 2.521 3.531 6.931 13.121
beta3_slope[11] 43.491 0.150 43.221 43.489 43.776
beta3_slope[12] 43.457 0.266 43.066 43.422 44.023
beta3_slope[13] 43.597 0.554 42.511 43.635 44.699
beta3_slope[14] 44.690 0.426 43.793 44.754 45.336
beta3_slope[15] 43.601 0.250 43.125 43.611 44.051
beta3_slope[16] 43.474 0.168 43.188 43.461 43.820
beta4_slope[11] -0.454 0.207 -0.863 -0.447 -0.062
beta4_slope[12] -1.151 0.655 -2.626 -1.066 -0.108
beta4_slope[13] 0.180 0.212 -0.214 0.179 0.599
beta4_slope[14] -0.121 0.247 -0.607 -0.119 0.351
beta4_slope[15] -0.199 0.198 -0.596 -0.203 0.185
beta4_slope[16] -0.122 0.222 -0.545 -0.122 0.306
sigma_H[1] 0.194 0.054 0.095 0.190 0.313
sigma_H[2] 0.172 0.030 0.120 0.170 0.238
sigma_H[3] 0.197 0.042 0.123 0.194 0.288
sigma_H[4] 0.419 0.077 0.293 0.410 0.597
sigma_H[5] 0.979 0.210 0.602 0.976 1.420
sigma_H[6] 0.396 0.202 0.042 0.387 0.833
sigma_H[7] 0.295 0.058 0.203 0.290 0.424
sigma_H[8] 0.424 0.092 0.284 0.415 0.626
sigma_H[9] 0.517 0.123 0.331 0.501 0.801
sigma_H[10] 0.217 0.043 0.142 0.214 0.312
sigma_H[11] 0.279 0.045 0.205 0.274 0.380
sigma_H[12] 0.443 0.165 0.212 0.425 0.773
sigma_H[13] 0.214 0.037 0.147 0.211 0.295
sigma_H[14] 0.505 0.093 0.346 0.497 0.707
sigma_H[15] 0.251 0.042 0.183 0.246 0.347
sigma_H[16] 0.223 0.042 0.150 0.219 0.314
lambda_H[1] 2.993 3.926 0.154 1.737 13.101
lambda_H[2] 8.347 7.899 0.843 6.046 29.213
lambda_H[3] 6.140 8.914 0.270 3.083 31.396
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 3.489 7.740 0.032 0.903 26.952
lambda_H[6] 7.740 15.187 0.008 1.106 54.949
lambda_H[7] 0.015 0.011 0.002 0.012 0.042
lambda_H[8] 8.378 10.584 0.004 4.626 38.534
lambda_H[9] 0.016 0.010 0.003 0.013 0.042
lambda_H[10] 0.309 0.596 0.032 0.196 1.111
lambda_H[11] 0.253 0.361 0.011 0.130 1.127
lambda_H[12] 5.104 6.562 0.187 2.764 24.018
lambda_H[13] 3.234 2.932 0.239 2.389 10.848
lambda_H[14] 3.611 4.343 0.238 2.217 15.069
lambda_H[15] 0.043 0.906 0.004 0.017 0.104
lambda_H[16] 0.981 1.208 0.054 0.542 4.460
mu_lambda_H[1] 4.391 1.937 1.255 4.221 8.522
mu_lambda_H[2] 3.816 1.939 0.673 3.650 7.980
mu_lambda_H[3] 3.512 1.880 0.750 3.237 7.775
sigma_lambda_H[1] 8.719 4.319 2.027 8.152 18.117
sigma_lambda_H[2] 8.254 4.607 1.175 7.731 18.161
sigma_lambda_H[3] 6.269 4.052 0.961 5.363 16.424
beta_H[1,1] 6.893 1.087 4.395 7.048 8.531
beta_H[2,1] 9.874 0.480 8.860 9.899 10.781
beta_H[3,1] 8.004 0.777 6.105 8.103 9.281
beta_H[4,1] 9.463 7.838 -6.567 9.502 24.248
beta_H[5,1] 0.068 2.424 -5.079 0.210 4.090
beta_H[6,1] 3.289 3.849 -6.306 4.663 7.780
beta_H[7,1] 1.466 5.610 -10.840 1.833 11.568
beta_H[8,1] 2.013 6.274 -2.466 1.235 21.060
beta_H[9,1] 13.124 5.591 1.901 13.128 23.982
beta_H[10,1] 7.067 1.674 3.443 7.151 10.262
beta_H[11,1] 5.247 3.437 -2.700 6.008 10.003
beta_H[12,1] 2.605 1.081 0.698 2.540 4.902
beta_H[13,1] 9.016 0.888 7.183 9.095 10.437
beta_H[14,1] 2.194 1.003 0.250 2.206 4.136
beta_H[15,1] -5.783 3.985 -13.135 -5.996 2.637
beta_H[16,1] 3.287 2.554 -0.827 2.993 9.449
beta_H[1,2] 7.906 0.245 7.400 7.910 8.369
beta_H[2,2] 10.022 0.134 9.767 10.021 10.290
beta_H[3,2] 8.955 0.205 8.551 8.953 9.366
beta_H[4,2] 3.520 1.461 0.785 3.496 6.571
beta_H[5,2] 1.954 0.956 0.008 1.979 3.773
beta_H[6,2] 5.793 1.098 3.248 6.011 7.466
beta_H[7,2] 2.365 1.088 0.414 2.266 4.746
beta_H[8,2] 2.834 1.638 -2.699 3.125 4.241
beta_H[9,2] 3.444 1.100 1.406 3.385 5.737
beta_H[10,2] 8.184 0.339 7.518 8.191 8.831
beta_H[11,2] 9.723 0.616 8.804 9.602 11.128
beta_H[12,2] 3.939 0.375 3.260 3.923 4.715
beta_H[13,2] 9.115 0.253 8.639 9.105 9.633
beta_H[14,2] 4.012 0.347 3.349 4.002 4.717
beta_H[15,2] 11.313 0.716 9.829 11.330 12.682
beta_H[16,2] 4.509 0.784 3.040 4.499 6.117
beta_H[1,3] 8.490 0.237 8.066 8.479 8.981
beta_H[2,3] 10.076 0.115 9.854 10.077 10.307
beta_H[3,3] 9.615 0.165 9.296 9.616 9.952
beta_H[4,3] -2.458 0.891 -4.249 -2.444 -0.713
beta_H[5,3] 3.891 0.613 2.632 3.903 5.040
beta_H[6,3] 8.123 1.211 6.552 7.735 10.837
beta_H[7,3] -2.450 0.732 -3.899 -2.439 -1.047
beta_H[8,3] 5.310 0.722 4.643 5.171 7.820
beta_H[9,3] -2.722 0.746 -4.219 -2.699 -1.328
beta_H[10,3] 8.739 0.269 8.223 8.737 9.256
beta_H[11,3] 8.544 0.281 7.934 8.564 9.029
beta_H[12,3] 5.230 0.326 4.446 5.272 5.746
beta_H[13,3] 8.841 0.178 8.490 8.843 9.191
beta_H[14,3] 5.687 0.273 5.089 5.707 6.175
beta_H[15,3] 10.392 0.332 9.730 10.393 11.026
beta_H[16,3] 6.283 0.577 5.070 6.349 7.246
beta_H[1,4] 8.280 0.176 7.903 8.291 8.598
beta_H[2,4] 10.135 0.121 9.869 10.144 10.352
beta_H[3,4] 10.120 0.167 9.749 10.133 10.404
beta_H[4,4] 11.771 0.444 10.905 11.778 12.642
beta_H[5,4] 5.567 0.784 4.303 5.463 7.430
beta_H[6,4] 7.192 0.897 5.106 7.478 8.385
beta_H[7,4] 8.187 0.346 7.503 8.186 8.864
beta_H[8,4] 6.666 0.318 5.804 6.698 7.121
beta_H[9,4] 7.195 0.464 6.280 7.185 8.094
beta_H[10,4] 7.765 0.236 7.323 7.759 8.250
beta_H[11,4] 9.292 0.209 8.899 9.288 9.710
beta_H[12,4] 7.124 0.215 6.716 7.118 7.564
beta_H[13,4] 9.006 0.146 8.714 9.011 9.284
beta_H[14,4] 7.668 0.217 7.266 7.664 8.097
beta_H[15,4] 9.454 0.247 8.985 9.454 9.936
beta_H[16,4] 9.244 0.230 8.836 9.229 9.751
beta_H[1,5] 8.976 0.146 8.672 8.982 9.249
beta_H[2,5] 10.779 0.094 10.599 10.775 10.977
beta_H[3,5] 10.925 0.172 10.620 10.917 11.285
beta_H[4,5] 8.401 0.457 7.531 8.389 9.331
beta_H[5,5] 5.381 0.597 4.002 5.442 6.414
beta_H[6,5] 8.748 0.602 7.893 8.605 10.298
beta_H[7,5] 6.814 0.331 6.154 6.809 7.453
beta_H[8,5] 8.221 0.260 7.843 8.189 8.905
beta_H[9,5] 8.213 0.473 7.237 8.221 9.125
beta_H[10,5] 10.080 0.227 9.638 10.076 10.516
beta_H[11,5] 11.535 0.232 11.079 11.536 11.993
beta_H[12,5] 8.473 0.203 8.085 8.469 8.891
beta_H[13,5] 10.009 0.134 9.737 10.010 10.273
beta_H[14,5] 9.192 0.230 8.777 9.182 9.681
beta_H[15,5] 11.169 0.249 10.678 11.174 11.646
beta_H[16,5] 9.954 0.171 9.604 9.957 10.282
beta_H[1,6] 10.184 0.191 9.854 10.170 10.593
beta_H[2,6] 11.510 0.107 11.299 11.511 11.713
beta_H[3,6] 10.814 0.167 10.451 10.825 11.114
beta_H[4,6] 12.861 0.813 11.108 12.886 14.441
beta_H[5,6] 5.927 0.612 4.787 5.919 7.196
beta_H[6,6] 8.808 0.645 7.053 8.914 9.758
beta_H[7,6] 9.806 0.550 8.728 9.807 10.902
beta_H[8,6] 9.496 0.353 8.741 9.536 9.955
beta_H[9,6] 8.465 0.789 6.896 8.466 10.125
beta_H[10,6] 9.518 0.318 8.832 9.541 10.078
beta_H[11,6] 10.808 0.353 10.068 10.832 11.425
beta_H[12,6] 9.374 0.249 8.902 9.365 9.874
beta_H[13,6] 11.061 0.163 10.774 11.055 11.413
beta_H[14,6] 9.875 0.288 9.311 9.875 10.447
beta_H[15,6] 10.870 0.437 10.040 10.867 11.777
beta_H[16,6] 10.544 0.231 10.055 10.557 10.985
beta_H[1,7] 10.856 0.887 8.667 10.982 12.251
beta_H[2,7] 12.213 0.428 11.328 12.229 13.017
beta_H[3,7] 10.543 0.663 9.110 10.598 11.684
beta_H[4,7] 2.529 4.143 -5.590 2.505 10.927
beta_H[5,7] 6.510 1.929 3.043 6.461 10.967
beta_H[6,7] 9.566 2.348 4.647 9.519 15.750
beta_H[7,7] 10.765 2.725 5.195 10.795 16.091
beta_H[8,7] 11.040 1.373 9.328 10.904 13.710
beta_H[9,7] 4.449 4.056 -3.989 4.468 12.432
beta_H[10,7] 9.838 1.455 7.128 9.729 13.057
beta_H[11,7] 10.998 1.750 7.724 10.853 14.857
beta_H[12,7] 10.014 0.927 7.992 10.105 11.504
beta_H[13,7] 11.647 0.782 9.871 11.747 12.855
beta_H[14,7] 10.483 0.936 8.518 10.547 12.179
beta_H[15,7] 12.115 2.282 7.610 12.053 16.571
beta_H[16,7] 12.191 1.213 10.164 12.033 14.996
beta0_H[1] 8.908 15.398 -17.977 8.647 37.138
beta0_H[2] 10.662 6.163 -2.479 10.847 22.529
beta0_H[3] 10.149 9.837 -9.502 9.985 30.766
beta0_H[4] 6.818 185.922 -371.931 5.732 388.642
beta0_H[5] 3.979 24.506 -50.585 4.586 48.227
beta0_H[6] 6.283 47.684 -99.100 7.563 110.943
beta0_H[7] 1.577 128.761 -269.349 2.372 263.028
beta0_H[8] 6.899 52.933 -25.731 6.429 35.729
beta0_H[9] 3.860 120.146 -239.748 1.649 242.410
beta0_H[10] 7.603 32.132 -60.173 8.701 73.276
beta0_H[11] 8.767 50.192 -92.794 9.707 115.465
beta0_H[12] 6.700 12.385 -17.275 6.742 29.394
beta0_H[13] 9.618 11.010 -10.937 9.864 30.136
beta0_H[14] 6.987 10.775 -15.133 7.045 28.055
beta0_H[15] 5.291 108.203 -225.431 6.881 219.536
beta0_H[16] 8.381 23.302 -40.572 8.031 58.444